Why does the Earth spin on its axis?

Earth spins on its axis due to the conservation of angular momentum. When two objects collide, unless they hit exactly head on, spin will be introduced to the system.

Imagine two people walk into each other. If they hit directly, they both come to a stop in front of each other. If they instead only clip their shoulders, they will spin slightly and move past one another. In space, almost nothing hits anything straight on, and these collisions impart spin because of their angular momentum. As there is no friction, normally these bodies will continue to spin unless they are pulled on by another object's gravity.